Question

The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively. Find:

1. the gradient of PQ;
2. the equation of PQ;
3. the co-ordinates of the point where PQ intersects the x-axis.

Answer 1

Given, co-ordinates of two points P and Q are (2, 6) and (–3, 5) respectively.

i. Gradient of PQ = ${\displaystyle \frac{5-6}{-3-2}=\frac{-1}{-5}=\frac{1}{5}}$

ii. The equation of the line PQ is given by:

y − y₁ = m(x − x₁)

${\displaystyle y-6=\frac{1}{5}(x-2)}$

5y − 30 = x − 2

5y = x + 28

iii. Let the line PQ intersects the x-axis at point A(x, 0).

Putting y = 0 in the equation of the line PQ, we get,

0 = x + 28

x = −28

Thus, the co-ordinates of the point where PQ intersects the x-axis are A(−28, 0).